EVENT DETAILS AND ABSTRACT

Title: Special metrics in hypercomplex Geometry
Speaker: Elia Fusi
Speaker Info: University of Turin
Brief Description:
Special Note:
Abstract:

The existence of special hyperhermitian metrics plays an important role in the study of hypercomplex manifolds. In this talk, after a brief overview of the basic definitions in hypercomplex Geometry, we will discuss two of the main types of special metrics in the hypercomplex setting: quaternionic Gauduchon and strong HKT metrics. First of all, we will discuss sufficient and equivalent conditions for a quaternionic Gauduchon metric to exist. Afterwards, we will show that strong HKT and balanced hyperhermitian metrics cannot coexist on a compact non-hyperKähler manifold, proving a particular instance of the Fino- Vezzoni conjecture. Finally, we will introduce an Einstein condition for hyperhermitian metrics and describe the similarities with the Kähler-Einstein case. This is a joint work with Giovanni Gentili.